LMFDB - Embedded newform 8007.2.a.g.1.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8007,2,Mod(1,8007)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8007, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0, 0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("8007.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8007 = 3 \cdot 17 \cdot 157 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8007.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$63.9362168984$
Analytic rank:	$0$
Dimension:	$56$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.10
Character	$\chi$	$=$	8007.1

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.95968 q^{2} -1.00000 q^{3} +1.84033 q^{4} -3.13690 q^{5} +1.95968 q^{6} -0.0823024 q^{7} +0.312893 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.95968 q^{2} -1.00000 q^{3} +1.84033 q^{4} -3.13690 q^{5} +1.95968 q^{6} -0.0823024 q^{7} +0.312893 q^{8} +1.00000 q^{9} +6.14731 q^{10} -4.24990 q^{11} -1.84033 q^{12} -4.08920 q^{13} +0.161286 q^{14} +3.13690 q^{15} -4.29384 q^{16} -1.00000 q^{17} -1.95968 q^{18} +7.68658 q^{19} -5.77294 q^{20} +0.0823024 q^{21} +8.32842 q^{22} -7.53627 q^{23} -0.312893 q^{24} +4.84012 q^{25} +8.01352 q^{26} -1.00000 q^{27} -0.151464 q^{28} -2.44445 q^{29} -6.14731 q^{30} +7.00948 q^{31} +7.78875 q^{32} +4.24990 q^{33} +1.95968 q^{34} +0.258174 q^{35} +1.84033 q^{36} +5.17174 q^{37} -15.0632 q^{38} +4.08920 q^{39} -0.981513 q^{40} -1.76151 q^{41} -0.161286 q^{42} -9.53138 q^{43} -7.82123 q^{44} -3.13690 q^{45} +14.7687 q^{46} +5.75425 q^{47} +4.29384 q^{48} -6.99323 q^{49} -9.48508 q^{50} +1.00000 q^{51} -7.52550 q^{52} -4.26781 q^{53} +1.95968 q^{54} +13.3315 q^{55} -0.0257518 q^{56} -7.68658 q^{57} +4.79033 q^{58} -13.6038 q^{59} +5.77294 q^{60} -13.8029 q^{61} -13.7363 q^{62} -0.0823024 q^{63} -6.67576 q^{64} +12.8274 q^{65} -8.32842 q^{66} -13.8314 q^{67} -1.84033 q^{68} +7.53627 q^{69} -0.505938 q^{70} -7.48735 q^{71} +0.312893 q^{72} +14.6676 q^{73} -10.1349 q^{74} -4.84012 q^{75} +14.1459 q^{76} +0.349777 q^{77} -8.01352 q^{78} +4.21154 q^{79} +13.4693 q^{80} +1.00000 q^{81} +3.45199 q^{82} +10.0865 q^{83} +0.151464 q^{84} +3.13690 q^{85} +18.6784 q^{86} +2.44445 q^{87} -1.32976 q^{88} -7.67701 q^{89} +6.14731 q^{90} +0.336551 q^{91} -13.8693 q^{92} -7.00948 q^{93} -11.2765 q^{94} -24.1120 q^{95} -7.78875 q^{96} -0.0337335 q^{97} +13.7045 q^{98} -4.24990 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q + q^{2} - 56 q^{3} + 61 q^{4} + q^{5} - q^{6} + 19 q^{7} + 56 q^{9}+O(q^{10}) $ 56 * q + q^2 - 56 * q^3 + 61 * q^4 + q^5 - q^6 + 19 * q^7 + 56 * q^9	\( 56 q + q^{2} - 56 q^{3} + 61 q^{4} + q^{5} - q^{6} + 19 q^{7} + 56 q^{9} + 8 q^{10} - 7 q^{11} - 61 q^{12} + 8 q^{13} - 8 q^{14} - q^{15} + 71 q^{16} - 56 q^{17} + q^{18} - 2 q^{19} - 4 q^{20} - 19 q^{21} + 47 q^{22} + 16 q^{23} + 85 q^{25} - 11 q^{26} - 56 q^{27} + 52 q^{28} + 17 q^{29} - 8 q^{30} + 23 q^{31} + 11 q^{32} + 7 q^{33} - q^{34} - 41 q^{35} + 61 q^{36} + 58 q^{37} - 22 q^{38} - 8 q^{39} + 38 q^{40} - q^{41} + 8 q^{42} + 27 q^{43} + 2 q^{44} + q^{45} + 46 q^{46} + 5 q^{47} - 71 q^{48} + 59 q^{49} - 4 q^{50} + 56 q^{51} + 25 q^{52} + 15 q^{53} - q^{54} + 9 q^{55} - 36 q^{56} + 2 q^{57} + 89 q^{58} - 61 q^{59} + 4 q^{60} + 47 q^{61} + 8 q^{62} + 19 q^{63} + 88 q^{64} + 39 q^{65} - 47 q^{66} + 20 q^{67} - 61 q^{68} - 16 q^{69} + 36 q^{70} - 2 q^{71} + 93 q^{73} + 48 q^{74} - 85 q^{75} + 38 q^{76} + 26 q^{77} + 11 q^{78} + 72 q^{79} + 42 q^{80} + 56 q^{81} + 33 q^{82} - 11 q^{83} - 52 q^{84} - q^{85} - 4 q^{86} - 17 q^{87} + 130 q^{88} - 6 q^{89} + 8 q^{90} + 37 q^{91} + 132 q^{92} - 23 q^{93} - 32 q^{94} + 12 q^{95} - 11 q^{96} + 100 q^{97} + 42 q^{98} - 7 q^{99}+O(q^{100}) \) 56 * q + q^2 - 56 * q^3 + 61 * q^4 + q^5 - q^6 + 19 * q^7 + 56 * q^9 + 8 * q^10 - 7 * q^11 - 61 * q^12 + 8 * q^13 - 8 * q^14 - q^15 + 71 * q^16 - 56 * q^17 + q^18 - 2 * q^19 - 4 * q^20 - 19 * q^21 + 47 * q^22 + 16 * q^23 + 85 * q^25 - 11 * q^26 - 56 * q^27 + 52 * q^28 + 17 * q^29 - 8 * q^30 + 23 * q^31 + 11 * q^32 + 7 * q^33 - q^34 - 41 * q^35 + 61 * q^36 + 58 * q^37 - 22 * q^38 - 8 * q^39 + 38 * q^40 - q^41 + 8 * q^42 + 27 * q^43 + 2 * q^44 + q^45 + 46 * q^46 + 5 * q^47 - 71 * q^48 + 59 * q^49 - 4 * q^50 + 56 * q^51 + 25 * q^52 + 15 * q^53 - q^54 + 9 * q^55 - 36 * q^56 + 2 * q^57 + 89 * q^58 - 61 * q^59 + 4 * q^60 + 47 * q^61 + 8 * q^62 + 19 * q^63 + 88 * q^64 + 39 * q^65 - 47 * q^66 + 20 * q^67 - 61 * q^68 - 16 * q^69 + 36 * q^70 - 2 * q^71 + 93 * q^73 + 48 * q^74 - 85 * q^75 + 38 * q^76 + 26 * q^77 + 11 * q^78 + 72 * q^79 + 42 * q^80 + 56 * q^81 + 33 * q^82 - 11 * q^83 - 52 * q^84 - q^85 - 4 * q^86 - 17 * q^87 + 130 * q^88 - 6 * q^89 + 8 * q^90 + 37 * q^91 + 132 * q^92 - 23 * q^93 - 32 * q^94 + 12 * q^95 - 11 * q^96 + 100 * q^97 + 42 * q^98 - 7 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	−1.95968	−1.38570	−0.692850	−	0.721081i	$-0.743645\pi$
$2$	−1.95968	−1.38570	−0.692850	+	0.721081i	$0.743645\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	1.84033	0.920167
$5$	−3.13690	−1.40286	−0.701431	−	0.712737i	$-0.747455\pi$
$5$	−3.13690	−1.40286	−0.701431	+	0.712737i	$0.747455\pi$
$6$	1.95968	0.800035
$7$	−0.0823024	−0.0311074	−0.0155537	−	0.999879i	$-0.504951\pi$
$7$	−0.0823024	−0.0311074	−0.0155537	+	0.999879i	$0.504951\pi$
$8$	0.312893	0.110624
$9$	1.00000	0.333333
$10$	6.14731	1.94395
$11$	−4.24990	−1.28139	−0.640696	−	0.767795i	$-0.721354\pi$
$11$	−4.24990	−1.28139	−0.640696	+	0.767795i	$0.721354\pi$
$12$	−1.84033	−0.531259
$13$	−4.08920	−1.13414	−0.567070	−	0.823669i	$-0.691923\pi$
$13$	−4.08920	−1.13414	−0.567070	+	0.823669i	$0.691923\pi$
$14$	0.161286	0.0431055
$15$	3.13690	0.809943
$16$	−4.29384	−1.07346
$17$	−1.00000	−0.242536
$17$	−1.00000	−0.242536
$18$	−1.95968	−0.461900
$19$	7.68658	1.76342	0.881712	−	0.471789i	$-0.156391\pi$
$19$	7.68658	1.76342	0.881712	+	0.471789i	$0.156391\pi$
$20$	−5.77294	−1.29087
$21$	0.0823024	0.0179599
$22$	8.32842	1.77563
$23$	−7.53627	−1.57142	−0.785711	−	0.618594i	$-0.787703\pi$
$23$	−7.53627	−1.57142	−0.785711	+	0.618594i	$0.787703\pi$
$24$	−0.312893	−0.0638690
$25$	4.84012	0.968025
$26$	8.01352	1.57158
$27$	−1.00000	−0.192450
$28$	−0.151464	−0.0286240
$29$	−2.44445	−0.453922	−0.226961	−	0.973904i	$-0.572879\pi$
$29$	−2.44445	−0.453922	−0.226961	+	0.973904i	$0.572879\pi$
$30$	−6.14731	−1.12234
$31$	7.00948	1.25894	0.629470	−	0.777025i	$-0.283272\pi$
$31$	7.00948	1.25894	0.629470	+	0.777025i	$0.283272\pi$
$32$	7.78875	1.37687
$33$	4.24990	0.739812
$34$	1.95968	0.336082
$35$	0.258174	0.0436394
$36$	1.84033	0.306722
$37$	5.17174	0.850228	0.425114	−	0.905140i	$-0.360234\pi$
$37$	5.17174	0.850228	0.425114	+	0.905140i	$0.360234\pi$
$38$	−15.0632	−2.44358
$39$	4.08920	0.654796
$40$	−0.981513	−0.155191
$41$	−1.76151	−0.275102	−0.137551	−	0.990495i	$-0.543923\pi$
$41$	−1.76151	−0.275102	−0.137551	+	0.990495i	$0.543923\pi$
$42$	−0.161286	−0.0248870
$43$	−9.53138	−1.45352	−0.726761	−	0.686891i	$-0.758975\pi$
$43$	−9.53138	−1.45352	−0.726761	+	0.686891i	$0.758975\pi$
$44$	−7.82123	−1.17909
$45$	−3.13690	−0.467621
$46$	14.7687	2.17752
$47$	5.75425	0.839344	0.419672	−	0.907676i	$-0.362145\pi$
$47$	5.75425	0.839344	0.419672	+	0.907676i	$0.362145\pi$
$48$	4.29384	0.619762
$49$	−6.99323	−0.999032
$50$	−9.48508	−1.34139
$51$	1.00000	0.140028
$52$	−7.52550	−1.04360
$53$	−4.26781	−0.586229	−0.293114	−	0.956077i	$-0.594692\pi$
$53$	−4.26781	−0.586229	−0.293114	+	0.956077i	$0.594692\pi$
$54$	1.95968	0.266678
$55$	13.3315	1.79762
$56$	−0.0257518	−0.00344123
$57$	−7.68658	−1.01811
$58$	4.79033	0.629001
$59$	−13.6038	−1.77107	−0.885535	−	0.464572i	$-0.846208\pi$
$59$	−13.6038	−1.77107	−0.885535	+	0.464572i	$0.846208\pi$
$60$	5.77294	0.745283
$61$	−13.8029	−1.76728	−0.883642	−	0.468162i	$-0.844916\pi$
$61$	−13.8029	−1.76728	−0.883642	+	0.468162i	$0.844916\pi$
$62$	−13.7363	−1.74451
$63$	−0.0823024	−0.0103691
$64$	−6.67576	−0.834470
$65$	12.8274	1.59104
$66$	−8.32842	−1.02516
$67$	−13.8314	−1.68977	−0.844886	−	0.534946i	$-0.820332\pi$
$67$	−13.8314	−1.68977	−0.844886	+	0.534946i	$0.820332\pi$
$68$	−1.84033	−0.223173
$69$	7.53627	0.907261
$70$	−0.505938	−0.0604711
$71$	−7.48735	−0.888585	−0.444293	−	0.895882i	$-0.646545\pi$
$71$	−7.48735	−0.888585	−0.444293	+	0.895882i	$0.646545\pi$
$72$	0.312893	0.0368748
$73$	14.6676	1.71671	0.858355	−	0.513056i	$-0.171487\pi$
$73$	14.6676	1.71671	0.858355	+	0.513056i	$0.171487\pi$
$74$	−10.1349	−1.17816
$75$	−4.84012	−0.558889
$76$	14.1459	1.62264
$77$	0.349777	0.0398607
$78$	−8.01352	−0.907352
$79$	4.21154	0.473836	0.236918	−	0.971530i	$-0.423863\pi$
$79$	4.21154	0.473836	0.236918	+	0.971530i	$0.423863\pi$
$80$	13.4693	1.50592
$81$	1.00000	0.111111
$82$	3.45199	0.381208
$83$	10.0865	1.10714	0.553571	−	0.832802i	$-0.313265\pi$
$83$	10.0865	1.10714	0.553571	+	0.832802i	$0.313265\pi$
$84$	0.151464	0.0165261
$85$	3.13690	0.340244
$86$	18.6784	2.01415
$87$	2.44445	0.262072
$88$	−1.32976	−0.141753
$89$	−7.67701	−0.813761	−0.406880	−	0.913481i	$-0.633383\pi$
$89$	−7.67701	−0.813761	−0.406880	+	0.913481i	$0.633383\pi$
$90$	6.14731	0.647983
$91$	0.336551	0.0352801
$92$	−13.8693	−1.44597
$93$	−7.00948	−0.726849
$94$	−11.2765	−1.16308
$95$	−24.1120	−2.47384
$96$	−7.78875	−0.794936
$97$	−0.0337335	−0.00342511	−0.00171256	−	0.999999i	$-0.500545\pi$
$97$	−0.0337335	−0.00342511	−0.00171256	+	0.999999i	$0.500545\pi$
$98$	13.7045	1.38436
$99$	−4.24990	−0.427131
$100$	8.90744	0.890744
$101$	−13.0043	−1.29397	−0.646987	−	0.762501i	$-0.723971\pi$
$101$	−13.0043	−1.29397	−0.646987	+	0.762501i	$0.723971\pi$
$102$	−1.95968	−0.194037
$103$	−5.89713	−0.581061	−0.290531	−	0.956866i	$-0.593832\pi$
$103$	−5.89713	−0.581061	−0.290531	+	0.956866i	$0.593832\pi$
$104$	−1.27948	−0.125464
$105$	−0.258174	−0.0251952
$106$	8.36353	0.812338
$107$	−5.84335	−0.564898	−0.282449	−	0.959282i	$-0.591147\pi$
$107$	−5.84335	−0.564898	−0.282449	+	0.959282i	$0.591147\pi$
$108$	−1.84033	−0.177086
$109$	−9.23906	−0.884941	−0.442471	−	0.896783i	$-0.645898\pi$
$109$	−9.23906	−0.884941	−0.442471	+	0.896783i	$0.645898\pi$
$110$	−26.1254	−2.49096
$111$	−5.17174	−0.490879
$112$	0.353393	0.0333925
$113$	17.8225	1.67660	0.838300	−	0.545209i	$-0.183550\pi$
$113$	17.8225	1.67660	0.838300	+	0.545209i	$0.183550\pi$
$114$	15.0632	1.41080
$115$	23.6405	2.20449
$116$	−4.49860	−0.417685
$117$	−4.08920	−0.378047
$118$	26.6592	2.45417
$119$	0.0823024	0.00754465
$120$	0.981513	0.0895994
$121$	7.06162	0.641965
$122$	27.0493	2.44893
$123$	1.76151	0.158830
$124$	12.8998	1.15844
$125$	0.501519	0.0448572
$126$	0.161286	0.0143685
$127$	−16.6611	−1.47843	−0.739216	−	0.673468i	$-0.764804\pi$
$127$	−16.6611	−1.47843	−0.739216	+	0.673468i	$0.764804\pi$
$128$	−2.49517	−0.220544
$129$	9.53138	0.839191
$130$	−25.1376	−2.20471
$131$	7.68272	0.671243	0.335621	−	0.941997i	$-0.391054\pi$
$131$	7.68272	0.671243	0.335621	+	0.941997i	$0.391054\pi$
$132$	7.82123	0.680751
$133$	−0.632624	−0.0548555
$134$	27.1050	2.34152
$135$	3.13690	0.269981
$136$	−0.312893	−0.0268303
$137$	−5.65056	−0.482760	−0.241380	−	0.970431i	$-0.577600\pi$
$137$	−5.65056	−0.482760	−0.241380	+	0.970431i	$0.577600\pi$
$138$	−14.7687	−1.25719
$139$	−7.00385	−0.594059	−0.297030	−	0.954868i	$-0.595996\pi$
$139$	−7.00385	−0.594059	−0.297030	+	0.954868i	$0.595996\pi$
$140$	0.475127	0.0401555
$141$	−5.75425	−0.484596
$142$	14.6728	1.23131
$143$	17.3787	1.45328
$144$	−4.29384	−0.357820
$145$	7.66798	0.636791
$146$	−28.7437	−2.37885
$147$	6.99323	0.576792
$148$	9.51772	0.782352
$149$	−18.4418	−1.51081	−0.755407	−	0.655256i	$-0.772561\pi$
$149$	−18.4418	−1.51081	−0.755407	+	0.655256i	$0.772561\pi$
$150$	9.48508	0.774453
$151$	12.1509	0.988825	0.494412	−	0.869227i	$-0.335383\pi$
$151$	12.1509	0.988825	0.494412	+	0.869227i	$0.335383\pi$
$152$	2.40508	0.195078
$153$	−1.00000	−0.0808452
$154$	−0.685449	−0.0552351
$155$	−21.9880	−1.76612
$156$	7.52550	0.602522
$157$	1.00000	0.0798087
$157$	1.00000	0.0798087
$158$	−8.25327	−0.656595
$159$	4.26781	0.338459
$160$	−24.4325	−1.93156
$161$	0.620253	0.0488828
$162$	−1.95968	−0.153967
$163$	17.3885	1.36197	0.680986	−	0.732296i	$-0.261551\pi$
$163$	17.3885	1.36197	0.680986	+	0.732296i	$0.261551\pi$
$164$	−3.24177	−0.253139
$165$	−13.3315	−1.03785
$166$	−19.7664	−1.53417
$167$	19.6152	1.51787	0.758934	−	0.651167i	$-0.225720\pi$
$167$	19.6152	1.51787	0.758934	+	0.651167i	$0.225720\pi$
$168$	0.0257518	0.00198680
$169$	3.72157	0.286275
$170$	−6.14731	−0.471477
$171$	7.68658	0.587808
$172$	−17.5409	−1.33748
$173$	−16.9413	−1.28802	−0.644012	−	0.765016i	$-0.722731\pi$
$173$	−16.9413	−1.28802	−0.644012	+	0.765016i	$0.722731\pi$
$174$	−4.79033	−0.363154
$175$	−0.398354	−0.0301127
$176$	18.2484	1.37552
$177$	13.6038	1.02253
$178$	15.0445	1.12763
$179$	10.7591	0.804171	0.402086	−	0.915602i	$-0.368285\pi$
$179$	10.7591	0.804171	0.402086	+	0.915602i	$0.368285\pi$
$180$	−5.77294	−0.430290
$181$	−16.1317	−1.19906	−0.599529	−	0.800353i	$-0.704645\pi$
$181$	−16.1317	−1.19906	−0.599529	+	0.800353i	$0.704645\pi$
$182$	−0.659531	−0.0488877
$183$	13.8029	1.02034
$184$	−2.35805	−0.173837
$185$	−16.2232	−1.19275
$186$	13.7363	1.00720
$187$	4.24990	0.310783
$188$	10.5898	0.772337
$189$	0.0823024	0.00598662
$190$	47.2518	3.42800
$191$	−25.8661	−1.87161	−0.935803	−	0.352523i	$-0.885324\pi$
$191$	−25.8661	−1.87161	−0.935803	+	0.352523i	$0.885324\pi$
$192$	6.67576	0.481781
$193$	−8.17982	−0.588796	−0.294398	−	0.955683i	$-0.595119\pi$
$193$	−8.17982	−0.588796	−0.294398	+	0.955683i	$0.595119\pi$
$194$	0.0661067	0.00474618
$195$	−12.8274	−0.918590
$196$	−12.8699	−0.919277
$197$	−1.69821	−0.120993	−0.0604964	−	0.998168i	$-0.519268\pi$
$197$	−1.69821	−0.120993	−0.0604964	+	0.998168i	$0.519268\pi$
$198$	8.32842	0.591875
$199$	−21.7555	−1.54220	−0.771102	−	0.636712i	$-0.780294\pi$
$199$	−21.7555	−1.54220	−0.771102	+	0.636712i	$0.780294\pi$
$200$	1.51444	0.107087
$201$	13.8314	0.975591
$202$	25.4842	1.79306
$203$	0.201184	0.0141203
$204$	1.84033	0.128849
$205$	5.52567	0.385930
$206$	11.5565	0.805177
$207$	−7.53627	−0.523807
$208$	17.5584	1.21745
$209$	−32.6672	−2.25964
$210$	0.505938	0.0349130
$211$	−23.7238	−1.63321	−0.816607	−	0.577194i	$-0.804148\pi$
$211$	−23.7238	−1.63321	−0.816607	+	0.577194i	$0.804148\pi$
$212$	−7.85420	−0.539429
$213$	7.48735	0.513025
$214$	11.4511	0.782780
$215$	29.8990	2.03909
$216$	−0.312893	−0.0212897
$217$	−0.576897	−0.0391623
$218$	18.1056	1.22626
$219$	−14.6676	−0.991143
$220$	24.5344	1.65411
$221$	4.08920	0.275069
$222$	10.1349	0.680212
$223$	−14.9701	−1.00247	−0.501237	−	0.865310i	$-0.667121\pi$
$223$	−14.9701	−1.00247	−0.501237	+	0.865310i	$0.667121\pi$
$224$	−0.641033	−0.0428308
$225$	4.84012	0.322675
$226$	−34.9263	−2.32327
$227$	−15.3451	−1.01849	−0.509246	−	0.860621i	$-0.670076\pi$
$227$	−15.3451	−1.01849	−0.509246	+	0.860621i	$0.670076\pi$
$228$	−14.1459	−0.936834
$229$	−10.2953	−0.680334	−0.340167	−	0.940365i	$-0.610484\pi$
$229$	−10.2953	−0.680334	−0.340167	+	0.940365i	$0.610484\pi$
$230$	−46.3278	−3.05476
$231$	−0.349777	−0.0230136
$232$	−0.764850	−0.0502149
$233$	−26.4963	−1.73583	−0.867916	−	0.496711i	$-0.834541\pi$
$233$	−26.4963	−1.73583	−0.867916	+	0.496711i	$0.834541\pi$
$234$	8.01352	0.523860
$235$	−18.0505	−1.17748
$236$	−25.0356	−1.62968
$237$	−4.21154	−0.273569
$238$	−0.161286	−0.0104546
$239$	−22.6597	−1.46573	−0.732867	−	0.680372i	$-0.761818\pi$
$239$	−22.6597	−1.46573	−0.732867	+	0.680372i	$0.761818\pi$
$240$	−13.4693	−0.869441
$241$	13.2143	0.851207	0.425604	−	0.904910i	$-0.360062\pi$
$241$	13.2143	0.851207	0.425604	+	0.904910i	$0.360062\pi$
$242$	−13.8385	−0.889572
$243$	−1.00000	−0.0641500
$244$	−25.4020	−1.62620
$245$	21.9370	1.40151
$246$	−3.45199	−0.220091
$247$	−31.4320	−1.99997
$248$	2.19322	0.139269
$249$	−10.0865	−0.639208
$250$	−0.982815	−0.0621587
$251$	−14.7430	−0.930567	−0.465284	−	0.885162i	$-0.654048\pi$
$251$	−14.7430	−0.930567	−0.465284	+	0.885162i	$0.654048\pi$
$252$	−0.151464	−0.00954133
$253$	32.0284	2.01361
$254$	32.6504	2.04867
$255$	−3.13690	−0.196440
$256$	18.2412	1.14008
$257$	−30.4695	−1.90063	−0.950316	−	0.311286i	$-0.899240\pi$
$257$	−30.4695	−1.90063	−0.950316	+	0.311286i	$0.899240\pi$
$258$	−18.6784	−1.16287
$259$	−0.425646	−0.0264484
$260$	23.6067	1.46403
$261$	−2.44445	−0.151307
$262$	−15.0557	−0.930142
$263$	8.90653	0.549200	0.274600	−	0.961559i	$-0.411455\pi$
$263$	8.90653	0.549200	0.274600	+	0.961559i	$0.411455\pi$
$264$	1.32976	0.0818412
$265$	13.3877	0.822399
$266$	1.23974	0.0760133
$267$	7.67701	0.469825
$268$	−25.4544	−1.55487
$269$	5.69097	0.346985	0.173492	−	0.984835i	$-0.444495\pi$
$269$	5.69097	0.346985	0.173492	+	0.984835i	$0.444495\pi$
$270$	−6.14731	−0.374113
$271$	−17.3290	−1.05266	−0.526330	−	0.850280i	$-0.676432\pi$
$271$	−17.3290	−1.05266	−0.526330	+	0.850280i	$0.676432\pi$
$272$	4.29384	0.260352
$273$	−0.336551	−0.0203690
$274$	11.0733	0.668961
$275$	−20.5700	−1.24042
$276$	13.8693	0.834832
$277$	−12.8864	−0.774267	−0.387133	−	0.922024i	$-0.626535\pi$
$277$	−12.8864	−0.774267	−0.387133	+	0.922024i	$0.626535\pi$
$278$	13.7253	0.823188
$279$	7.00948	0.419647
$280$	0.0807808	0.00482758
$281$	−9.52336	−0.568116	−0.284058	−	0.958807i	$-0.591681\pi$
$281$	−9.52336	−0.568116	−0.284058	+	0.958807i	$0.591681\pi$
$282$	11.2765	0.671505
$283$	11.3545	0.674953	0.337476	−	0.941334i	$-0.390427\pi$
$283$	11.3545	0.674953	0.337476	+	0.941334i	$0.390427\pi$
$284$	−13.7792	−0.817647
$285$	24.1120	1.42827
$286$	−34.0566	−2.01381
$287$	0.144976	0.00855769
$288$	7.78875	0.458957
$289$	1.00000	0.0588235
$290$	−15.0268	−0.882402
$291$	0.0337335	0.00197749
$292$	26.9933	1.57966
$293$	12.7010	0.742003	0.371002	−	0.928632i	$-0.379014\pi$
$293$	12.7010	0.742003	0.371002	+	0.928632i	$0.379014\pi$
$294$	−13.7045	−0.799261
$295$	42.6739	2.48457
$296$	1.61820	0.0940559
$297$	4.24990	0.246604
$298$	36.1400	2.09354
$299$	30.8173	1.78221
$300$	−8.90744	−0.514272
$301$	0.784455	0.0452153
$302$	−23.8118	−1.37022
$303$	13.0043	0.747077
$304$	−33.0049	−1.89296
$305$	43.2984	2.47926
$306$	1.95968	0.112027
$307$	31.1950	1.78039	0.890197	−	0.455576i	$-0.150567\pi$
$307$	31.1950	1.78039	0.890197	+	0.455576i	$0.150567\pi$
$308$	0.643706	0.0366786
$309$	5.89713	0.335476
$310$	43.0894	2.44732
$311$	−22.8343	−1.29482	−0.647408	−	0.762144i	$-0.724147\pi$
$311$	−22.8343	−1.29482	−0.647408	+	0.762144i	$0.724147\pi$
$312$	1.27948	0.0724364
$313$	23.0003	1.30006	0.650028	−	0.759910i	$-0.274757\pi$
$313$	23.0003	1.30006	0.650028	+	0.759910i	$0.274757\pi$
$314$	−1.95968	−0.110591
$315$	0.258174	0.0145465
$316$	7.75065	0.436008
$317$	−17.8599	−1.00311	−0.501556	−	0.865125i	$-0.667239\pi$
$317$	−17.8599	−1.00311	−0.501556	+	0.865125i	$0.667239\pi$
$318$	−8.36353	−0.469003
$319$	10.3886	0.581653
$320$	20.9412	1.17065
$321$	5.84335	0.326144
$322$	−1.21550	−0.0677370
$323$	−7.68658	−0.427693
$324$	1.84033	0.102241
$325$	−19.7922	−1.09788
$326$	−34.0759	−1.88729
$327$	9.23906	0.510921
$328$	−0.551164	−0.0304329
$329$	−0.473589	−0.0261098
$330$	26.1254	1.43816
$331$	6.94918	0.381962	0.190981	−	0.981594i	$-0.438833\pi$
$331$	6.94918	0.381962	0.190981	+	0.981594i	$0.438833\pi$
$332$	18.5626	1.01876
$333$	5.17174	0.283409
$334$	−38.4394	−2.10331
$335$	43.3876	2.37052
$336$	−0.353393	−0.0192792
$337$	−13.3874	−0.729260	−0.364630	−	0.931152i	$-0.618805\pi$
$337$	−13.3874	−0.729260	−0.364630	+	0.931152i	$0.618805\pi$
$338$	−7.29308	−0.396691
$339$	−17.8225	−0.967985
$340$	5.77294	0.313082
$341$	−29.7896	−1.61320
$342$	−15.0632	−0.814526
$343$	1.15168	0.0621847
$344$	−2.98230	−0.160795
$345$	−23.6405	−1.27276
$346$	33.1995	1.78482
$347$	−20.7033	−1.11141	−0.555706	−	0.831379i	$-0.687552\pi$
$347$	−20.7033	−1.11141	−0.555706	+	0.831379i	$0.687552\pi$
$348$	4.49860	0.241150
$349$	0.884993	0.0473726	0.0236863	−	0.999719i	$-0.492460\pi$
$349$	0.884993	0.0473726	0.0236863	+	0.999719i	$0.492460\pi$
$350$	0.780645	0.0417272
$351$	4.08920	0.218265
$352$	−33.1014	−1.76431
$353$	−22.7449	−1.21059	−0.605296	−	0.796001i	$-0.706945\pi$
$353$	−22.7449	−1.21059	−0.605296	+	0.796001i	$0.706945\pi$
$354$	−26.6592	−1.41692
$355$	23.4871	1.24656
$356$	−14.1283	−0.748796
$357$	−0.0823024	−0.00435590
$358$	−21.0843	−1.11434
$359$	19.7135	1.04044	0.520219	−	0.854033i	$-0.325850\pi$
$359$	19.7135	1.04044	0.520219	+	0.854033i	$0.325850\pi$
$360$	−0.981513	−0.0517303
$361$	40.0836	2.10966
$362$	31.6129	1.66154
$363$	−7.06162	−0.370639
$364$	0.619367	0.0324636
$365$	−46.0107	−2.40831
$366$	−27.0493	−1.41389
$367$	2.35319	0.122836	0.0614179	−	0.998112i	$-0.480438\pi$
$367$	2.35319	0.122836	0.0614179	+	0.998112i	$0.480438\pi$
$368$	32.3595	1.68686
$369$	−1.76151	−0.0917005
$370$	31.7922	1.65280
$371$	0.351251	0.0182360
$372$	−12.8998	−0.668823
$373$	−18.7378	−0.970204	−0.485102	−	0.874457i	$-0.661218\pi$
$373$	−18.7378	−0.970204	−0.485102	+	0.874457i	$0.661218\pi$
$374$	−8.32842	−0.430653
$375$	−0.501519	−0.0258983
$376$	1.80046	0.0928519
$377$	9.99584	0.514812
$378$	−0.161286	−0.00829566
$379$	3.49665	0.179611	0.0898053	−	0.995959i	$-0.471376\pi$
$379$	3.49665	0.179611	0.0898053	+	0.995959i	$0.471376\pi$
$380$	−44.3742	−2.27635
$381$	16.6611	0.853573
$382$	50.6892	2.59349
$383$	3.07130	0.156936	0.0784679	−	0.996917i	$-0.474997\pi$
$383$	3.07130	0.156936	0.0784679	+	0.996917i	$0.474997\pi$
$384$	2.49517	0.127331
$385$	−1.09721	−0.0559192
$386$	16.0298	0.815896
$387$	−9.53138	−0.484507
$388$	−0.0620809	−0.00315168
$389$	−21.6227	−1.09632	−0.548158	−	0.836375i	$-0.684671\pi$
$389$	−21.6227	−1.09632	−0.548158	+	0.836375i	$0.684671\pi$
$390$	25.1376	1.27289
$391$	7.53627	0.381126
$392$	−2.18813	−0.110517
$393$	−7.68272	−0.387542
$394$	3.32795	0.167660
$395$	−13.2112	−0.664727
$396$	−7.82123	−0.393032
$397$	7.39012	0.370900	0.185450	−	0.982654i	$-0.440626\pi$
$397$	7.39012	0.370900	0.185450	+	0.982654i	$0.440626\pi$
$398$	42.6337	2.13703
$399$	0.632624	0.0316708
$400$	−20.7827	−1.03914
$401$	33.2780	1.66182	0.830912	−	0.556404i	$-0.187819\pi$
$401$	33.2780	1.66182	0.830912	+	0.556404i	$0.187819\pi$
$402$	−27.1050	−1.35188
$403$	−28.6632	−1.42782
$404$	−23.9322	−1.19067
$405$	−3.13690	−0.155874
$406$	−0.394255	−0.0195666
$407$	−21.9793	−1.08948
$408$	0.312893	0.0154905
$409$	22.5337	1.11422	0.557110	−	0.830439i	$-0.311910\pi$
$409$	22.5337	1.11422	0.557110	+	0.830439i	$0.311910\pi$
$410$	−10.8285	−0.534783
$411$	5.65056	0.278722
$412$	−10.8527	−0.534673
$413$	1.11963	0.0550934
$414$	14.7687	0.725840
$415$	−31.6404	−1.55317
$416$	−31.8498	−1.56156
$417$	7.00385	0.342980
$418$	64.0171	3.13118
$419$	13.3030	0.649896	0.324948	−	0.945732i	$-0.394653\pi$
$419$	13.3030	0.649896	0.324948	+	0.945732i	$0.394653\pi$
$420$	−0.475127	−0.0231838
$421$	−3.34851	−0.163196	−0.0815982	−	0.996665i	$-0.526002\pi$
$421$	−3.34851	−0.163196	−0.0815982	+	0.996665i	$0.526002\pi$
$422$	46.4910	2.26315
$423$	5.75425	0.279781
$424$	−1.33537	−0.0648512
$425$	−4.84012	−0.234780
$426$	−14.6728	−0.710899
$427$	1.13601	0.0549756
$428$	−10.7537	−0.519801
$429$	−17.3787	−0.839051
$430$	−58.5923	−2.82557
$431$	5.13523	0.247355	0.123678	−	0.992322i	$-0.460531\pi$
$431$	5.13523	0.247355	0.123678	+	0.992322i	$0.460531\pi$
$432$	4.29384	0.206587
$433$	14.9939	0.720561	0.360281	−	0.932844i	$-0.382681\pi$
$433$	14.9939	0.720561	0.360281	+	0.932844i	$0.382681\pi$
$434$	1.13053	0.0542673
$435$	−7.66798	−0.367651
$436$	−17.0030	−0.814294
$437$	−57.9282	−2.77108
$438$	28.7437	1.37343
$439$	37.1806	1.77453	0.887266	−	0.461258i	$-0.152602\pi$
$439$	37.1806	1.77453	0.887266	+	0.461258i	$0.152602\pi$
$440$	4.17133	0.198860
$441$	−6.99323	−0.333011
$442$	−8.01352	−0.381164
$443$	26.0096	1.23576	0.617878	−	0.786274i	$-0.287993\pi$
$443$	26.0096	1.23576	0.617878	+	0.786274i	$0.287993\pi$
$444$	−9.51772	−0.451691
$445$	24.0820	1.14160
$446$	29.3366	1.38913
$447$	18.4418	0.872269
$448$	0.549431	0.0259582
$449$	−24.2680	−1.14528	−0.572638	−	0.819808i	$-0.694080\pi$
$449$	−24.2680	−1.14528	−0.572638	+	0.819808i	$0.694080\pi$
$450$	−9.48508	−0.447131
$451$	7.48623	0.352513
$452$	32.7994	1.54275
$453$	−12.1509	−0.570898
$454$	30.0715	1.41133
$455$	−1.05573	−0.0494932
$456$	−2.40508	−0.112628
$457$	−1.05432	−0.0493190	−0.0246595	−	0.999696i	$-0.507850\pi$
$457$	−1.05432	−0.0493190	−0.0246595	+	0.999696i	$0.507850\pi$
$458$	20.1755	0.942739
$459$	1.00000	0.0466760
$460$	43.5065	2.02850
$461$	−5.62437	−0.261953	−0.130976	−	0.991385i	$-0.541811\pi$
$461$	−5.62437	−0.261953	−0.130976	+	0.991385i	$0.541811\pi$
$462$	0.685449	0.0318900
$463$	6.20270	0.288264	0.144132	−	0.989558i	$-0.453961\pi$
$463$	6.20270	0.288264	0.144132	+	0.989558i	$0.453961\pi$
$464$	10.4961	0.487267
$465$	21.9880	1.01967
$466$	51.9242	2.40534
$467$	7.89423	0.365302	0.182651	−	0.983178i	$-0.441532\pi$
$467$	7.89423	0.365302	0.182651	+	0.983178i	$0.441532\pi$
$468$	−7.52550	−0.347866
$469$	1.13836	0.0525644
$470$	35.3732	1.63164
$471$	−1.00000	−0.0460776
$472$	−4.25655	−0.195923
$473$	40.5074	1.86253
$474$	8.25327	0.379085
$475$	37.2040	1.70704
$476$	0.151464	0.00694234
$477$	−4.26781	−0.195410
$478$	44.4057	2.03107
$479$	42.7616	1.95383	0.976913	−	0.213639i	$-0.0685317\pi$
$479$	42.7616	1.95383	0.976913	+	0.213639i	$0.0685317\pi$
$480$	24.4325	1.11519
$481$	−21.1483	−0.964278
$482$	−25.8957	−1.17952
$483$	−0.620253	−0.0282225
$484$	12.9957	0.590715
$485$	0.105818	0.00480497
$486$	1.95968	0.0888928
$487$	−13.6099	−0.616725	−0.308362	−	0.951269i	$-0.599781\pi$
$487$	−13.6099	−0.616725	−0.308362	+	0.951269i	$0.599781\pi$
$488$	−4.31884	−0.195505
$489$	−17.3885	−0.786335
$490$	−42.9895	−1.94207
$491$	−15.0892	−0.680966	−0.340483	−	0.940251i	$-0.610591\pi$
$491$	−15.0892	−0.680966	−0.340483	+	0.940251i	$0.610591\pi$
$492$	3.24177	0.146150
$493$	2.44445	0.110092
$494$	61.5966	2.77136
$495$	13.3315	0.599206
$496$	−30.0976	−1.35142
$497$	0.616227	0.0276416
$498$	19.7664	0.885752
$499$	−10.9229	−0.488976	−0.244488	−	0.969652i	$-0.578620\pi$
$499$	−10.9229	−0.488976	−0.244488	+	0.969652i	$0.578620\pi$
$500$	0.922962	0.0412761
$501$	−19.6152	−0.876342
$502$	28.8914	1.28949
$503$	10.8848	0.485331	0.242666	−	0.970110i	$-0.421978\pi$
$503$	10.8848	0.485331	0.242666	+	0.970110i	$0.421978\pi$
$504$	−0.0257518	−0.00114708
$505$	40.7931	1.81527
$506$	−62.7653	−2.79026
$507$	−3.72157	−0.165281
$508$	−30.6620	−1.36041
$509$	15.7744	0.699187	0.349593	−	0.936902i	$-0.386320\pi$
$509$	15.7744	0.699187	0.349593	+	0.936902i	$0.386320\pi$
$510$	6.14731	0.272207
$511$	−1.20718	−0.0534024
$512$	−30.7566	−1.35926
$513$	−7.68658	−0.339371
$514$	59.7103	2.63371
$515$	18.4987	0.815149
$516$	17.5409	0.772196
$517$	−24.4550	−1.07553
$518$	0.834129	0.0366495
$519$	16.9413	0.743641
$520$	4.01360	0.176008
$521$	−4.93175	−0.216064	−0.108032	−	0.994147i	$-0.534455\pi$
$521$	−4.93175	−0.216064	−0.108032	+	0.994147i	$0.534455\pi$
$522$	4.79033	0.209667
$523$	−11.1727	−0.488547	−0.244274	−	0.969706i	$-0.578550\pi$
$523$	−11.1727	−0.488547	−0.244274	+	0.969706i	$0.578550\pi$
$524$	14.1388	0.617656
$525$	0.398354	0.0173856
$526$	−17.4539	−0.761027
$527$	−7.00948	−0.305338
$528$	−18.2484	−0.794158
$529$	33.7954	1.46937
$530$	−26.2355	−1.13960
$531$	−13.6038	−0.590357
$532$	−1.16424	−0.0504762
$533$	7.20317	0.312004
$534$	−15.0445	−0.651037
$535$	18.3300	0.792474
$536$	−4.32774	−0.186930
$537$	−10.7591	−0.464289
$538$	−11.1525	−0.480817
$539$	29.7205	1.28015
$540$	5.77294	0.248428
$541$	36.1516	1.55428	0.777140	−	0.629328i	$-0.216670\pi$
$541$	36.1516	1.55428	0.777140	+	0.629328i	$0.216670\pi$
$542$	33.9592	1.45867
$543$	16.1317	0.692276
$544$	−7.78875	−0.333940
$545$	28.9820	1.24145
$546$	0.659531	0.0282253
$547$	−8.59448	−0.367474	−0.183737	−	0.982975i	$-0.558819\pi$
$547$	−8.59448	−0.367474	−0.183737	+	0.982975i	$0.558819\pi$
$548$	−10.3989	−0.444220
$549$	−13.8029	−0.589095
$550$	40.3106	1.71885
$551$	−18.7895	−0.800457
$552$	2.35805	0.100365
$553$	−0.346620	−0.0147398
$554$	25.2531	1.07290
$555$	16.2232	0.688637
$556$	−12.8894	−0.546634
$557$	27.8515	1.18011	0.590054	−	0.807364i	$-0.299107\pi$
$557$	27.8515	1.18011	0.590054	+	0.807364i	$0.299107\pi$
$558$	−13.7363	−0.581505
$559$	38.9757	1.64850
$560$	−1.10856	−0.0468451
$561$	−4.24990	−0.179431
$562$	18.6627	0.787239
$563$	−1.83101	−0.0771677	−0.0385839	−	0.999255i	$-0.512285\pi$
$563$	−1.83101	−0.0771677	−0.0385839	+	0.999255i	$0.512285\pi$
$564$	−10.5898	−0.445909
$565$	−55.9073	−2.35204
$566$	−22.2511	−0.935283
$567$	−0.0823024	−0.00345638
$568$	−2.34274	−0.0982992
$569$	−29.1718	−1.22294	−0.611472	−	0.791266i	$-0.709422\pi$
$569$	−29.1718	−1.22294	−0.611472	+	0.791266i	$0.709422\pi$
$570$	−47.2518	−1.97916
$571$	35.1502	1.47099	0.735495	−	0.677530i	$-0.236949\pi$
$571$	35.1502	1.47099	0.735495	+	0.677530i	$0.236949\pi$
$572$	31.9826	1.33726
$573$	25.8661	1.08057
$574$	−0.284107	−0.0118584
$575$	−36.4765	−1.52117
$576$	−6.67576	−0.278157
$577$	−28.7245	−1.19582	−0.597908	−	0.801565i	$-0.704001\pi$
$577$	−28.7245	−1.19582	−0.597908	+	0.801565i	$0.704001\pi$
$578$	−1.95968	−0.0815118
$579$	8.17982	0.339942
$580$	14.1116	0.585954
$581$	−0.830146	−0.0344403
$582$	−0.0661067	−0.00274021
$583$	18.1377	0.751189
$584$	4.58938	0.189910
$585$	12.8274	0.530348
$586$	−24.8900	−1.02819
$587$	1.77764	0.0733711	0.0366856	−	0.999327i	$-0.488320\pi$
$587$	1.77764	0.0733711	0.0366856	+	0.999327i	$0.488320\pi$
$588$	12.8699	0.530745
$589$	53.8790	2.22004
$590$	−83.6270	−3.44287
$591$	1.69821	0.0698552
$592$	−22.2066	−0.912686
$593$	34.4055	1.41286	0.706431	−	0.707781i	$-0.250304\pi$
$593$	34.4055	1.41286	0.706431	+	0.707781i	$0.250304\pi$
$594$	−8.32842	−0.341719
$595$	−0.258174	−0.0105841
$596$	−33.9391	−1.39020
$597$	21.7555	0.890392
$598$	−60.3920	−2.46961
$599$	3.00734	0.122877	0.0614384	−	0.998111i	$-0.480431\pi$
$599$	3.00734	0.122877	0.0614384	+	0.998111i	$0.480431\pi$
$600$	−1.51444	−0.0618267
$601$	32.0678	1.30807	0.654036	−	0.756464i	$-0.273075\pi$
$601$	32.0678	1.30807	0.654036	+	0.756464i	$0.273075\pi$
$602$	−1.53728	−0.0626548
$603$	−13.8314	−0.563257
$604$	22.3617	0.909884
$605$	−22.1516	−0.900589
$606$	−25.4842	−1.03522
$607$	4.62862	0.187870	0.0939350	−	0.995578i	$-0.470055\pi$
$607$	4.62862	0.187870	0.0939350	+	0.995578i	$0.470055\pi$
$608$	59.8689	2.42800
$609$	−0.201184	−0.00815238
$610$	−84.8509	−3.43551
$611$	−23.5303	−0.951934
$612$	−1.84033	−0.0743911
$613$	6.23043	0.251645	0.125822	−	0.992053i	$-0.459843\pi$
$613$	6.23043	0.251645	0.125822	+	0.992053i	$0.459843\pi$
$614$	−61.1322	−2.46709
$615$	−5.52567	−0.222817
$616$	0.109443	0.00440957
$617$	3.27662	0.131912	0.0659558	−	0.997823i	$-0.478990\pi$
$617$	3.27662	0.131912	0.0659558	+	0.997823i	$0.478990\pi$
$618$	−11.5565	−0.464869
$619$	−17.6675	−0.710117	−0.355059	−	0.934844i	$-0.615539\pi$
$619$	−17.6675	−0.710117	−0.355059	+	0.934844i	$0.615539\pi$
$620$	−40.4653	−1.62513
$621$	7.53627	0.302420
$622$	44.7479	1.79423
$623$	0.631836	0.0253140
$624$	−17.5584	−0.702897
$625$	−25.7738	−1.03095
$626$	−45.0732	−1.80149
$627$	32.6672	1.30460
$628$	1.84033	0.0734373
$629$	−5.17174	−0.206211
$630$	−0.505938	−0.0201570
$631$	−46.2317	−1.84045	−0.920227	−	0.391384i	$-0.871996\pi$
$631$	−46.2317	−1.84045	−0.920227	+	0.391384i	$0.871996\pi$
$632$	1.31776	0.0524178
$633$	23.7238	0.942937
$634$	34.9996	1.39001
$635$	52.2641	2.07404
$636$	7.85420	0.311439
$637$	28.5967	1.13304
$638$	−20.3584	−0.805997
$639$	−7.48735	−0.296195
$640$	7.82708	0.309392
$641$	−22.0358	−0.870363	−0.435182	−	0.900343i	$-0.643316\pi$
$641$	−22.0358	−0.870363	−0.435182	+	0.900343i	$0.643316\pi$
$642$	−11.4511	−0.451938
$643$	−33.7886	−1.33249	−0.666246	−	0.745732i	$-0.732100\pi$
$643$	−33.7886	−1.33249	−0.666246	+	0.745732i	$0.732100\pi$
$644$	1.14147	0.0449804
$645$	−29.8990	−1.17727
$646$	15.0632	0.592655
$647$	−5.73902	−0.225624	−0.112812	−	0.993616i	$-0.535986\pi$
$647$	−5.73902	−0.225624	−0.112812	+	0.993616i	$0.535986\pi$
$648$	0.312893	0.0122916
$649$	57.8149	2.26944
$650$	38.7864	1.52133
$651$	0.576897	0.0226104
$652$	32.0007	1.25324
$653$	8.21217	0.321367	0.160684	−	0.987006i	$-0.448630\pi$
$653$	8.21217	0.321367	0.160684	+	0.987006i	$0.448630\pi$
$654$	−18.1056	−0.707984
$655$	−24.0999	−0.941662
$656$	7.56363	0.295310
$657$	14.6676	0.572237
$658$	0.928081	0.0361804
$659$	−45.7017	−1.78029	−0.890144	−	0.455680i	$-0.849396\pi$
$659$	−45.7017	−1.78029	−0.890144	+	0.455680i	$0.849396\pi$
$660$	−24.5344	−0.955000
$661$	−43.8977	−1.70742	−0.853712	−	0.520745i	$-0.825654\pi$
$661$	−43.8977	−1.70742	−0.853712	+	0.520745i	$0.825654\pi$
$662$	−13.6182	−0.529285
$663$	−4.08920	−0.158811
$664$	3.15601	0.122477
$665$	1.98448	0.0769547
$666$	−10.1349	−0.392721
$667$	18.4220	0.713304
$668$	36.0985	1.39669
$669$	14.9701	0.578778
$670$	−85.0257	−3.28483
$671$	58.6610	2.26458
$672$	0.641033	0.0247284
$673$	−28.3699	−1.09358	−0.546790	−	0.837270i	$-0.684151\pi$
$673$	−28.3699	−1.09358	−0.546790	+	0.837270i	$0.684151\pi$
$674$	26.2350	1.01054
$675$	−4.84012	−0.186296
$676$	6.84894	0.263421
$677$	38.3614	1.47435	0.737175	−	0.675702i	$-0.236159\pi$
$677$	38.3614	1.47435	0.737175	+	0.675702i	$0.236159\pi$
$678$	34.9263	1.34134
$679$	0.00277634	0.000106546 0
$680$	0.981513	0.0376393
$681$	15.3451	0.588027
$682$	58.3779	2.23541
$683$	4.36654	0.167081	0.0835404	−	0.996504i	$-0.473377\pi$
$683$	4.36654	0.167081	0.0835404	+	0.996504i	$0.473377\pi$
$684$	14.1459	0.540881
$685$	17.7252	0.677246
$686$	−2.25691	−0.0861693
$687$	10.2953	0.392791
$688$	40.9262	1.56030
$689$	17.4519	0.664866
$690$	46.3278	1.76367
$691$	23.2137	0.883092	0.441546	−	0.897239i	$-0.354430\pi$
$691$	23.2137	0.883092	0.441546	+	0.897239i	$0.354430\pi$
$692$	−31.1777	−1.18520
$693$	0.349777	0.0132869
$694$	40.5718	1.54009
$695$	21.9704	0.833384
$696$	0.764850	0.0289916
$697$	1.76151	0.0667219
$698$	−1.73430	−0.0656443
$699$	26.4963	1.00218
$700$	−0.733104	−0.0277087
$701$	−12.7567	−0.481815	−0.240907	−	0.970548i	$-0.577445\pi$
$701$	−12.7567	−0.481815	−0.240907	+	0.970548i	$0.577445\pi$
$702$	−8.01352	−0.302451
$703$	39.7530	1.49931
$704$	28.3713	1.06928
$705$	18.0505	0.679821
$706$	44.5727	1.67752
$707$	1.07028	0.0402522
$708$	25.0356	0.940897
$709$	47.5729	1.78664	0.893320	−	0.449422i	$-0.148370\pi$
$709$	47.5729	1.78664	0.893320	+	0.449422i	$0.148370\pi$
$710$	−46.0270	−1.72736
$711$	4.21154	0.157945
$712$	−2.40208	−0.0900217
$713$	−52.8254	−1.97833
$714$	0.161286	0.00603598
$715$	−54.5151	−2.03875
$716$	19.8003	0.739972
$717$	22.6597	0.846242
$718$	−38.6321	−1.44174
$719$	3.87228	0.144412	0.0722059	−	0.997390i	$-0.476996\pi$
$719$	3.87228	0.144412	0.0722059	+	0.997390i	$0.476996\pi$
$720$	13.4693	0.501972
$721$	0.485348	0.0180753
$722$	−78.5509	−2.92336
$723$	−13.2143	−0.491445
$724$	−29.6877	−1.10333
$725$	−11.8314	−0.439408
$726$	13.8385	0.513595
$727$	−9.18710	−0.340731	−0.170365	−	0.985381i	$-0.554495\pi$
$727$	−9.18710	−0.340731	−0.170365	+	0.985381i	$0.554495\pi$
$728$	0.105304	0.00390284
$729$	1.00000	0.0370370
$730$	90.1661	3.33720
$731$	9.53138	0.352531
$732$	25.4020	0.938886
$733$	−17.0021	−0.627988	−0.313994	−	0.949425i	$-0.601667\pi$
$733$	−17.0021	−0.627988	−0.313994	+	0.949425i	$0.601667\pi$
$734$	−4.61150	−0.170214
$735$	−21.9370	−0.809160
$736$	−58.6982	−2.16364
$737$	58.7819	2.16526
$738$	3.45199	0.127069
$739$	−46.8642	−1.72393	−0.861964	−	0.506970i	$-0.830765\pi$
$739$	−46.8642	−1.72393	−0.861964	+	0.506970i	$0.830765\pi$
$740$	−29.8561	−1.09753
$741$	31.4320	1.15468
$742$	−0.688338	−0.0252697
$743$	34.7217	1.27381	0.636907	−	0.770941i	$-0.280213\pi$
$743$	34.7217	1.27381	0.636907	+	0.770941i	$0.280213\pi$
$744$	−2.19322	−0.0804072
$745$	57.8501	2.11947
$746$	36.7200	1.34441
$747$	10.0865	0.369047
$748$	7.82123	0.285973
$749$	0.480922	0.0175725
$750$	0.982815	0.0358873
$751$	15.7179	0.573553	0.286776	−	0.957998i	$-0.407416\pi$
$751$	15.7179	0.573553	0.286776	+	0.957998i	$0.407416\pi$
$752$	−24.7078	−0.901002
$753$	14.7430	0.537263
$754$	−19.5886	−0.713375
$755$	−38.1161	−1.38719
$756$	0.151464	0.00550869
$757$	40.2038	1.46123	0.730615	−	0.682789i	$-0.239233\pi$
$757$	40.2038	1.46123	0.730615	+	0.682789i	$0.239233\pi$
$758$	−6.85230	−0.248887
$759$	−32.0284	−1.16256
$760$	−7.54448	−0.273667
$761$	12.6786	0.459600	0.229800	−	0.973238i	$-0.426193\pi$
$761$	12.6786	0.459600	0.229800	+	0.973238i	$0.426193\pi$
$762$	−32.6504	−1.18280
$763$	0.760397	0.0275282
$764$	−47.6023	−1.72219
$765$	3.13690	0.113415
$766$	−6.01875	−0.217466
$767$	55.6289	2.00864
$768$	−18.2412	−0.658224
$769$	−46.2023	−1.66610	−0.833050	−	0.553198i	$-0.813407\pi$
$769$	−46.2023	−1.66610	−0.833050	+	0.553198i	$0.813407\pi$
$770$	2.15018	0.0774872
$771$	30.4695	1.09733
$772$	−15.0536	−0.541791
$773$	1.70719	0.0614034	0.0307017	−	0.999529i	$-0.490226\pi$
$773$	1.70719	0.0614034	0.0307017	+	0.999529i	$0.490226\pi$
$774$	18.6784	0.671382
$775$	33.9268	1.21868
$776$	−0.0105550	−0.000378901 0
$777$	0.425646	0.0152700
$778$	42.3736	1.51917
$779$	−13.5400	−0.485120
$780$	−23.6067	−0.845256
$781$	31.8205	1.13863
$782$	−14.7687	−0.528126
$783$	2.44445	0.0873574
$784$	30.0278	1.07242
$785$	−3.13690	−0.111961
$786$	15.0557	0.537018
$787$	−0.794826	−0.0283325	−0.0141662	−	0.999900i	$-0.504509\pi$
$787$	−0.794826	−0.0283325	−0.0141662	+	0.999900i	$0.504509\pi$
$788$	−3.12528	−0.111334
$789$	−8.90653	−0.317081
$790$	25.8896	0.921112
$791$	−1.46683	−0.0521546
$792$	−1.32976	−0.0472510
$793$	56.4430	2.00435
$794$	−14.4823	−0.513956
$795$	−13.3877	−0.474812
$796$	−40.0373	−1.41909
$797$	−0.400916	−0.0142012	−0.00710059	−	0.999975i	$-0.502260\pi$
$797$	−0.400916	−0.0142012	−0.00710059	+	0.999975i	$0.502260\pi$
$798$	−1.23974	−0.0438863
$799$	−5.75425	−0.203571
$800$	37.6985	1.33284
$801$	−7.67701	−0.271254
$802$	−65.2141	−2.30279
$803$	−62.3357	−2.19978
$804$	25.4544	0.897707
$805$	−1.94567	−0.0685759
$806$	56.1706	1.97852
$807$	−5.69097	−0.200332
$808$	−4.06895	−0.143145
$809$	27.6667	0.972710	0.486355	−	0.873761i	$-0.338326\pi$
$809$	27.6667	0.972710	0.486355	+	0.873761i	$0.338326\pi$
$810$	6.14731	0.215994
$811$	−33.4664	−1.17517	−0.587583	−	0.809164i	$-0.699920\pi$
$811$	−33.4664	−1.17517	−0.587583	+	0.809164i	$0.699920\pi$
$812$	0.370246	0.0129931
$813$	17.3290	0.607754
$814$	43.0724	1.50969
$815$	−54.5459	−1.91066
$816$	−4.29384	−0.150314
$817$	−73.2637	−2.56317
$818$	−44.1588	−1.54398
$819$	0.336551	0.0117600
$820$	10.1691	0.355120
$821$	33.3720	1.16469	0.582345	−	0.812942i	$-0.302135\pi$
$821$	33.3720	1.16469	0.582345	+	0.812942i	$0.302135\pi$
$822$	−11.0733	−0.386225
$823$	4.85096	0.169094	0.0845469	−	0.996419i	$-0.473056\pi$
$823$	4.85096	0.169094	0.0845469	+	0.996419i	$0.473056\pi$
$824$	−1.84517	−0.0642795
$825$	20.5700	0.716156
$826$	−2.19411	−0.0763429
$827$	6.20633	0.215815	0.107908	−	0.994161i	$-0.465585\pi$
$827$	6.20633	0.215815	0.107908	+	0.994161i	$0.465585\pi$
$828$	−13.8693	−0.481990
$829$	−24.8384	−0.862672	−0.431336	−	0.902191i	$-0.641958\pi$
$829$	−24.8384	−0.862672	−0.431336	+	0.902191i	$0.641958\pi$
$830$	62.0050	2.15223
$831$	12.8864	0.447023
$832$	27.2985	0.946406
$833$	6.99323	0.242301
$834$	−13.7253	−0.475268
$835$	−61.5308	−2.12936
$836$	−60.1185	−2.07924
$837$	−7.00948	−0.242283
$838$	−26.0697	−0.900561
$839$	14.1173	0.487385	0.243692	−	0.969853i	$-0.421641\pi$
$839$	14.1173	0.487385	0.243692	+	0.969853i	$0.421641\pi$
$840$	−0.0807808	−0.00278720
$841$	−23.0247	−0.793954
$842$	6.56200	0.226141
$843$	9.52336	0.328002
$844$	−43.6597	−1.50283
$845$	−11.6742	−0.401604
$846$	−11.2765	−0.387693
$847$	−0.581188	−0.0199699
$848$	18.3253	0.629293
$849$	−11.3545	−0.389684
$850$	9.48508	0.325335
$851$	−38.9756	−1.33607
$852$	13.7792	0.472069
$853$	−8.36946	−0.286565	−0.143282	−	0.989682i	$-0.545766\pi$
$853$	−8.36946	−0.286565	−0.143282	+	0.989682i	$0.545766\pi$
$854$	−2.22622	−0.0761797
$855$	−24.1120	−0.824614
$856$	−1.82834	−0.0624914
$857$	21.9416	0.749512	0.374756	−	0.927124i	$-0.377727\pi$
$857$	21.9416	0.749512	0.374756	+	0.927124i	$0.377727\pi$
$858$	34.0566	1.16267
$859$	−8.29194	−0.282917	−0.141459	−	0.989944i	$-0.545179\pi$
$859$	−8.29194	−0.282917	−0.141459	+	0.989944i	$0.545179\pi$
$860$	55.0241	1.87631
$861$	−0.144976	−0.00494078
$862$	−10.0634	−0.342760
$863$	15.7397	0.535786	0.267893	−	0.963449i	$-0.413673\pi$
$863$	15.7397	0.535786	0.267893	+	0.963449i	$0.413673\pi$
$864$	−7.78875	−0.264979
$865$	53.1431	1.80692
$866$	−29.3832	−0.998482
$867$	−1.00000	−0.0339618
$868$	−1.06168	−0.0360359
$869$	−17.8986	−0.607169
$870$	15.0268	0.509455
$871$	56.5593	1.91644
$872$	−2.89084	−0.0978960
$873$	−0.0337335	−0.00114170
$874$	113.521	3.83989
$875$	−0.0412762	−0.00139539
$876$	−26.9933	−0.912018
$877$	−8.09244	−0.273262	−0.136631	−	0.990622i	$-0.543628\pi$
$877$	−8.09244	−0.273262	−0.136631	+	0.990622i	$0.543628\pi$
$878$	−72.8619	−2.45897
$879$	−12.7010	−0.428396
$880$	−57.2432	−1.92967
$881$	15.1984	0.512048	0.256024	−	0.966670i	$-0.417587\pi$
$881$	15.1984	0.512048	0.256024	+	0.966670i	$0.417587\pi$
$882$	13.7045	0.461453
$883$	40.5042	1.36308	0.681538	−	0.731783i	$-0.261311\pi$
$883$	40.5042	1.36308	0.681538	+	0.731783i	$0.261311\pi$
$884$	7.52550	0.253110
$885$	−42.6739	−1.43447
$886$	−50.9705	−1.71239
$887$	28.1191	0.944147	0.472074	−	0.881559i	$-0.343506\pi$
$887$	28.1191	0.944147	0.472074	+	0.881559i	$0.343506\pi$
$888$	−1.61820	−0.0543032
$889$	1.37125	0.0459902
$890$	−47.1929	−1.58191
$891$	−4.24990	−0.142377
$892$	−27.5500	−0.922443
$893$	44.2306	1.48012
$894$	−36.1400	−1.20870
$895$	−33.7501	−1.12814
$896$	0.205358	0.00686053
$897$	−30.8173	−1.02896
$898$	47.5574	1.58701
$899$	−17.1343	−0.571461
$900$	8.90744	0.296915
$901$	4.26781	0.142181
$902$	−14.6706	−0.488477
$903$	−0.784455	−0.0261050
$904$	5.57653	0.185473
$905$	50.6034	1.68211
$906$	23.8118	0.791094
$907$	36.3544	1.20713	0.603564	−	0.797314i	$-0.293747\pi$
$907$	36.3544	1.20713	0.603564	+	0.797314i	$0.293747\pi$
$908$	−28.2402	−0.937183
$909$	−13.0043	−0.431325
$910$	2.06888	0.0685828
$911$	−47.5518	−1.57546	−0.787730	−	0.616021i	$-0.788744\pi$
$911$	−47.5518	−1.57546	−0.787730	+	0.616021i	$0.788744\pi$
$912$	33.0049	1.09290
$913$	−42.8667	−1.41868
$914$	2.06613	0.0683414
$915$	−43.2984	−1.43140
$916$	−18.9468	−0.626021
$917$	−0.632307	−0.0208806
$918$	−1.95968	−0.0646790
$919$	−27.5942	−0.910250	−0.455125	−	0.890427i	$-0.650405\pi$
$919$	−27.5942	−0.910250	−0.455125	+	0.890427i	$0.650405\pi$
$920$	7.39695	0.243870
$921$	−31.1950	−1.02791
$922$	11.0219	0.362988
$923$	30.6173	1.00778
$924$	−0.643706	−0.0211764
$925$	25.0318	0.823042
$926$	−12.1553	−0.399448
$927$	−5.89713	−0.193687
$928$	−19.0392	−0.624992
$929$	29.2953	0.961148	0.480574	−	0.876954i	$-0.340428\pi$
$929$	29.2953	0.961148	0.480574	+	0.876954i	$0.340428\pi$
$930$	−43.0894	−1.41296
$931$	−53.7540	−1.76172
$932$	−48.7621	−1.59726
$933$	22.8343	0.747562
$934$	−15.4701	−0.506199
$935$	−13.3315	−0.435986
$936$	−1.27948	−0.0418212
$937$	−12.7075	−0.415135	−0.207568	−	0.978221i	$-0.566555\pi$
$937$	−12.7075	−0.415135	−0.207568	+	0.978221i	$0.566555\pi$
$938$	−2.23081	−0.0728385
$939$	−23.0003	−0.750587
$940$	−33.2190	−1.08348
$941$	45.6448	1.48798	0.743988	−	0.668193i	$-0.232932\pi$
$941$	45.6448	1.48798	0.743988	+	0.668193i	$0.232932\pi$
$942$	1.95968	0.0638497
$943$	13.2752	0.432301
$944$	58.4127	1.90117
$945$	−0.258174	−0.00839840
$946$	−79.3814	−2.58091
$947$	25.7772	0.837646	0.418823	−	0.908068i	$-0.362443\pi$
$947$	25.7772	0.837646	0.418823	+	0.908068i	$0.362443\pi$
$948$	−7.75065	−0.251729
$949$	−59.9787	−1.94699
$950$	−72.9078	−2.36544
$951$	17.8599	0.579146
$952$	0.0257518	0.000834622 0
$953$	1.28480	0.0416189	0.0208095	−	0.999783i	$-0.493376\pi$
$953$	1.28480	0.0416189	0.0208095	+	0.999783i	$0.493376\pi$
$954$	8.36353	0.270779
$955$	81.1393	2.62561
$956$	−41.7014	−1.34872
$957$	−10.3886	−0.335817
$958$	−83.7988	−2.70742
$959$	0.465055	0.0150174
$960$	−20.9412	−0.675873
$961$	18.1328	0.584930
$962$	41.4438	1.33620
$963$	−5.84335	−0.188299
$964$	24.3187	0.783253
$965$	25.6593	0.826000
$966$	1.21550	0.0391080
$967$	−8.13900	−0.261733	−0.130866	−	0.991400i	$-0.541776\pi$
$967$	−8.13900	−0.261733	−0.130866	+	0.991400i	$0.541776\pi$
$968$	2.20953	0.0710170
$969$	7.68658	0.246929
$970$	−0.207370	−0.00665825
$971$	19.4448	0.624014	0.312007	−	0.950080i	$-0.398999\pi$
$971$	19.4448	0.624014	0.312007	+	0.950080i	$0.398999\pi$
$972$	−1.84033	−0.0590288
$973$	0.576434	0.0184796
$974$	26.6711	0.854596
$975$	19.7922	0.633859
$976$	59.2676	1.89711
$977$	47.2500	1.51166	0.755830	−	0.654768i	$-0.227233\pi$
$977$	47.2500	1.51166	0.755830	+	0.654768i	$0.227233\pi$
$978$	34.0759	1.08963
$979$	32.6265	1.04275
$980$	40.3715	1.28962
$981$	−9.23906	−0.294980
$982$	29.5700	0.943615
$983$	−13.6535	−0.435478	−0.217739	−	0.976007i	$-0.569868\pi$
$983$	−13.6535	−0.435478	−0.217739	+	0.976007i	$0.569868\pi$
$984$	0.551164	0.0175705
$985$	5.32712	0.169736
$986$	−4.79033	−0.152555
$987$	0.473589	0.0150745
$988$	−57.8454	−1.84031
$989$	71.8311	2.28410
$990$	−26.1254	−0.830320
$991$	−5.89208	−0.187168	−0.0935840	−	0.995611i	$-0.529832\pi$
$991$	−5.89208	−0.187168	−0.0935840	+	0.995611i	$0.529832\pi$
$992$	54.5951	1.73340
$993$	−6.94918	−0.220526
$994$	−1.20761	−0.0383029
$995$	68.2447	2.16350
$996$	−18.5626	−0.588179
$997$	−39.4712	−1.25007	−0.625033	−	0.780598i	$-0.714914\pi$
$997$	−39.4712	−1.25007	−0.625033	+	0.780598i	$0.714914\pi$
$998$	21.4054	0.677575
$999$	−5.17174	−0.163626

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8007.2.a.g.1.10	✓	56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8007.2.a.g.1.10	✓	56	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 8007 = 3 \cdot 17 \cdot 157 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8007.a (trivial)

\(f(q)\)	\(=\)	\(q-1.95968 q^{2} -1.00000 q^{3} +1.84033 q^{4} -3.13690 q^{5} +1.95968 q^{6} -0.0823024 q^{7} +0.312893 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.95968 q^{2} -1.00000 q^{3} +1.84033 q^{4} -3.13690 q^{5} +1.95968 q^{6} -0.0823024 q^{7} +0.312893 q^{8} +1.00000 q^{9} +6.14731 q^{10} -4.24990 q^{11} -1.84033 q^{12} -4.08920 q^{13} +0.161286 q^{14} +3.13690 q^{15} -4.29384 q^{16} -1.00000 q^{17} -1.95968 q^{18} +7.68658 q^{19} -5.77294 q^{20} +0.0823024 q^{21} +8.32842 q^{22} -7.53627 q^{23} -0.312893 q^{24} +4.84012 q^{25} +8.01352 q^{26} -1.00000 q^{27} -0.151464 q^{28} -2.44445 q^{29} -6.14731 q^{30} +7.00948 q^{31} +7.78875 q^{32} +4.24990 q^{33} +1.95968 q^{34} +0.258174 q^{35} +1.84033 q^{36} +5.17174 q^{37} -15.0632 q^{38} +4.08920 q^{39} -0.981513 q^{40} -1.76151 q^{41} -0.161286 q^{42} -9.53138 q^{43} -7.82123 q^{44} -3.13690 q^{45} +14.7687 q^{46} +5.75425 q^{47} +4.29384 q^{48} -6.99323 q^{49} -9.48508 q^{50} +1.00000 q^{51} -7.52550 q^{52} -4.26781 q^{53} +1.95968 q^{54} +13.3315 q^{55} -0.0257518 q^{56} -7.68658 q^{57} +4.79033 q^{58} -13.6038 q^{59} +5.77294 q^{60} -13.8029 q^{61} -13.7363 q^{62} -0.0823024 q^{63} -6.67576 q^{64} +12.8274 q^{65} -8.32842 q^{66} -13.8314 q^{67} -1.84033 q^{68} +7.53627 q^{69} -0.505938 q^{70} -7.48735 q^{71} +0.312893 q^{72} +14.6676 q^{73} -10.1349 q^{74} -4.84012 q^{75} +14.1459 q^{76} +0.349777 q^{77} -8.01352 q^{78} +4.21154 q^{79} +13.4693 q^{80} +1.00000 q^{81} +3.45199 q^{82} +10.0865 q^{83} +0.151464 q^{84} +3.13690 q^{85} +18.6784 q^{86} +2.44445 q^{87} -1.32976 q^{88} -7.67701 q^{89} +6.14731 q^{90} +0.336551 q^{91} -13.8693 q^{92} -7.00948 q^{93} -11.2765 q^{94} -24.1120 q^{95} -7.78875 q^{96} -0.0337335 q^{97} +13.7045 q^{98} -4.24990 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q + q^{2} - 56 q^{3} + 61 q^{4} + q^{5} - q^{6} + 19 q^{7} + 56 q^{9}+O(q^{10}) \) 56 * q + q^2 - 56 * q^3 + 61 * q^4 + q^5 - q^6 + 19 * q^7 + 56 * q^9	\( 56 q + q^{2} - 56 q^{3} + 61 q^{4} + q^{5} - q^{6} + 19 q^{7} + 56 q^{9} + 8 q^{10} - 7 q^{11} - 61 q^{12} + 8 q^{13} - 8 q^{14} - q^{15} + 71 q^{16} - 56 q^{17} + q^{18} - 2 q^{19} - 4 q^{20} - 19 q^{21} + 47 q^{22} + 16 q^{23} + 85 q^{25} - 11 q^{26} - 56 q^{27} + 52 q^{28} + 17 q^{29} - 8 q^{30} + 23 q^{31} + 11 q^{32} + 7 q^{33} - q^{34} - 41 q^{35} + 61 q^{36} + 58 q^{37} - 22 q^{38} - 8 q^{39} + 38 q^{40} - q^{41} + 8 q^{42} + 27 q^{43} + 2 q^{44} + q^{45} + 46 q^{46} + 5 q^{47} - 71 q^{48} + 59 q^{49} - 4 q^{50} + 56 q^{51} + 25 q^{52} + 15 q^{53} - q^{54} + 9 q^{55} - 36 q^{56} + 2 q^{57} + 89 q^{58} - 61 q^{59} + 4 q^{60} + 47 q^{61} + 8 q^{62} + 19 q^{63} + 88 q^{64} + 39 q^{65} - 47 q^{66} + 20 q^{67} - 61 q^{68} - 16 q^{69} + 36 q^{70} - 2 q^{71} + 93 q^{73} + 48 q^{74} - 85 q^{75} + 38 q^{76} + 26 q^{77} + 11 q^{78} + 72 q^{79} + 42 q^{80} + 56 q^{81} + 33 q^{82} - 11 q^{83} - 52 q^{84} - q^{85} - 4 q^{86} - 17 q^{87} + 130 q^{88} - 6 q^{89} + 8 q^{90} + 37 q^{91} + 132 q^{92} - 23 q^{93} - 32 q^{94} + 12 q^{95} - 11 q^{96} + 100 q^{97} + 42 q^{98} - 7 q^{99}+O(q^{100}) \) 56 * q + q^2 - 56 * q^3 + 61 * q^4 + q^5 - q^6 + 19 * q^7 + 56 * q^9 + 8 * q^10 - 7 * q^11 - 61 * q^12 + 8 * q^13 - 8 * q^14 - q^15 + 71 * q^16 - 56 * q^17 + q^18 - 2 * q^19 - 4 * q^20 - 19 * q^21 + 47 * q^22 + 16 * q^23 + 85 * q^25 - 11 * q^26 - 56 * q^27 + 52 * q^28 + 17 * q^29 - 8 * q^30 + 23 * q^31 + 11 * q^32 + 7 * q^33 - q^34 - 41 * q^35 + 61 * q^36 + 58 * q^37 - 22 * q^38 - 8 * q^39 + 38 * q^40 - q^41 + 8 * q^42 + 27 * q^43 + 2 * q^44 + q^45 + 46 * q^46 + 5 * q^47 - 71 * q^48 + 59 * q^49 - 4 * q^50 + 56 * q^51 + 25 * q^52 + 15 * q^53 - q^54 + 9 * q^55 - 36 * q^56 + 2 * q^57 + 89 * q^58 - 61 * q^59 + 4 * q^60 + 47 * q^61 + 8 * q^62 + 19 * q^63 + 88 * q^64 + 39 * q^65 - 47 * q^66 + 20 * q^67 - 61 * q^68 - 16 * q^69 + 36 * q^70 - 2 * q^71 + 93 * q^73 + 48 * q^74 - 85 * q^75 + 38 * q^76 + 26 * q^77 + 11 * q^78 + 72 * q^79 + 42 * q^80 + 56 * q^81 + 33 * q^82 - 11 * q^83 - 52 * q^84 - q^85 - 4 * q^86 - 17 * q^87 + 130 * q^88 - 6 * q^89 + 8 * q^90 + 37 * q^91 + 132 * q^92 - 23 * q^93 - 32 * q^94 + 12 * q^95 - 11 * q^96 + 100 * q^97 + 42 * q^98 - 7 * q^99

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